LUXURY — 6 letters
For the six-letter opening, trace LUXURY from L at row 2, column 4. Move left to U at row 2, column 3, down to X at row 3, column 3, then left to U at row 3, column 2. Finish by going up to R at row 2, column 2 and up again to Y at row 1, column 2. Read the selected letters as L, U, X, U, R, Y.
The two Us sit on opposite sides of the X in the spelling, with a downward step before X and a leftward step after it. Keep that distinction when checking your trace. The route never moves right: its five moves are left, down, left, up, up, with three turns. It spans three rows and three columns, visiting the outer edge only at its final Y. These six cells leave 34 open cells for the other four words.